in bidding on a piece of land and we know one other bidder is interested. The se
ID: 3371093 • Letter: I
Question
in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,00 will be accept Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $14,800 a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)? b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)? c what amount should you bid to masinize the probability that you get the sropety tn dollan)? 03 d. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friendsu your objective is to maximize the expected profit, what is your bid? Bid $13000 to maximice the expected profit What is the expected profit for this bid (in dollars)?Explanation / Answer
a) (12,000-10,000)*1/(14,800-10,000)=2000/4800=0.42(round to 2 decimals).
b) (14,000-10,000)*1/(14,800-10,800)=4000/4800=0.83(round to 2 decimals )
c) To maximize probability of getting property one must bid 14,801$.
d) Expected profit:
(16,000-Bid) *P(You get the property with bid) =(16,000-Bid) *(Bid -10,000)/(14,800-10,000)
So, Expected profit if I use 14801$:
(16,000-14,801)*(14,801-10,000)/(14,800-10,000)=$1199.2498
Expected Profit if I use 13,000$ according to my friend's advice:
(16,000-13,000)*(13,000-10,000)/(14,800-10,000)=$1875.
So Bid $13,000 to maximize expected profit.
For this bid, Expected profit: $1875.
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